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Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3?
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Two particles of equal mass are connected to a rope AB of negligible m...
Given:
- Two particles of equal mass are connected to a rope AB of negligible mass.
- One particle is located at end A and the other is located at a point on the rope that divides the length in the ratio 1:2 from A.
To find:
The ratio of the tension in the smaller part of the rope to the tension in the larger part.
Assumption:
- The rope is being rotated about a point in a horizontal plane.
- The effect of gravity is ignored.
Explanation:
To solve this problem, we can consider the motion of the two particles separately and then analyze the forces acting on each of them.
1. Particle at the end A:
- The particle at the end A is rotating in a circular path with a radius equal to the length of the rope.
- The tension in the rope at point A provides the centripetal force required for circular motion.
- Let's denote the tension in the rope at point A as T1.
2. Particle at the dividing point:
- The particle located at the point dividing the rope in the ratio 1:2 from A is also rotating in a circular path.
- However, the radius of this circular path is only two-thirds of the length of the rope.
- The tension in the rope at this point provides the centripetal force required for circular motion.
- Let's denote the tension in the rope at this point as T2.
Analysis of forces:
- The particle at the end A experiences two forces: tension T1 and the force of the rope pulling it towards the center.
- The particle at the dividing point experiences two forces: tension T2 and the force of the rope pulling it towards the center.
- Since both particles have the same mass, the forces acting on them must be equal in magnitude.
Using the above analysis, we can conclude:
- The force of the rope pulling the particle at the dividing point towards the center is greater than the force of the rope pulling the particle at the end A towards the center.
- Therefore, the tension in the smaller part of the rope (T2) is greater than the tension in the larger part of the rope (T1).
Final answer:
The ratio of the tension in the smaller part of the rope to the tension in the larger part is 1:2. Hence, the correct option is C) 1:2.
- Two particles of equal mass are connected to a rope AB of negligible mass.
- One particle is located at end A and the other is located at a point on the rope that divides the length in the ratio 1:2 from A.
To find:
The ratio of the tension in the smaller part of the rope to the tension in the larger part.
Assumption:
- The rope is being rotated about a point in a horizontal plane.
- The effect of gravity is ignored.
Explanation:
To solve this problem, we can consider the motion of the two particles separately and then analyze the forces acting on each of them.
1. Particle at the end A:
- The particle at the end A is rotating in a circular path with a radius equal to the length of the rope.
- The tension in the rope at point A provides the centripetal force required for circular motion.
- Let's denote the tension in the rope at point A as T1.
2. Particle at the dividing point:
- The particle located at the point dividing the rope in the ratio 1:2 from A is also rotating in a circular path.
- However, the radius of this circular path is only two-thirds of the length of the rope.
- The tension in the rope at this point provides the centripetal force required for circular motion.
- Let's denote the tension in the rope at this point as T2.
Analysis of forces:
- The particle at the end A experiences two forces: tension T1 and the force of the rope pulling it towards the center.
- The particle at the dividing point experiences two forces: tension T2 and the force of the rope pulling it towards the center.
- Since both particles have the same mass, the forces acting on them must be equal in magnitude.
Using the above analysis, we can conclude:
- The force of the rope pulling the particle at the dividing point towards the center is greater than the force of the rope pulling the particle at the end A towards the center.
- Therefore, the tension in the smaller part of the rope (T2) is greater than the tension in the larger part of the rope (T1).
Final answer:
The ratio of the tension in the smaller part of the rope to the tension in the larger part is 1:2. Hence, the correct option is C) 1:2.
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Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3?
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Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3?.
Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3?.
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Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3?, a detailed solution for Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? has been provided alongside types of Two particles of equal mass are connected to a rope AB of negligible mass such that one is at the end A and other dividing the length of a rope in the ratio 1 is to 2 from A the Rope is rotated about and be in a horizontal plane ratio of the tension in the smaller part to the other is (ignore the effect of gravity) A 4:3 B 1:4 C 1:2 D 1:3? theory, EduRev gives you an
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